Method for generating distributions and classes of probability distributions: the univariate case

Year 2019, Volume: 48 Issue: 3, 897 - 930, 15.06.2019

Cicero Ramos De Brito Leandro Chaves Rego Wilson Rosa De Oliveira Frank Gomes-silva

Abstract

In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens the process of probability distribution construction. In this method, distribution classes are built from pre-defined monotonic functions and from known distributions. With its use, we can obtain different classes of probability distributions described in literature. Beside these results, we obtain results on the support and nature of the generated distributions.

Keywords

Probabilistic distributions generating method, Distribution classes generating functions, probabilistic distributions classes, probabilistic distribution support

References

• Alzaatreh, A., Lee, C. and Famoye F. A new method for generating families of continuous distributions, Metron 71, 63-79, 2013.
• Brito, C.R., Gomes-Silva, F., Rˆego, L.C. and Oliveira, W.R. A new class of gamma distribution, Acta Sci-Technol 39, 79-89, 2017.
• Cordeiro, G.M., Alizadeh, M. and Silva, R.B. A New Wider Family of Continuous Models: The Extended Cordeiro and de Castro Family, Hacet J Math Stat, 2017, In press.
• Cordeiro, G.M. and de Castro, M. A new family of generalized distributions, J Stat Comput Simul 81, 883-898, 2011.
• Consul, P.C. and Famoye, F. Lagrangian Probability Distributions, Birkhauser Boston, Boston, 2006.
• Eugene, N., Lee, C. and Famoye, F. Beta-normal distribution and its application, Commun Stat Theor Meth 31, 497-512, 2002.
• Gomes-Silva, F., Percontini, A., Brito, E., Ramos, M.W.A., Silva, R.V. and Cordeiro, G.M. The odd Lindley-G family of distributions, Austrian J Stat 49, 57-79,2017.
• Jayakumar, K. and Mathew, T. On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution, Stat Pap 49, 421-439, 2008.
• Lee, C., Famoye, F. and Alzaatreh, A. Methods for generating families of univariate continuous distributions in the recent decades, WIREs Comput Stat 5, 219-238, 2013.
• Marshall, A.W. and Olkin, I.A. A new method for adding a parameter to a family of distributions with application to the exponential and weibull families, Biometrika 84, 641-652, 1997.
• McDonald, J.B. Some generalized functions for the size distribution of income, Econometrica 52, 647-663, 1984.
• Mudholkar, G.S., Srivastava, D. K. and Freimer, M. The Exponentiated Weibull Family: A Reanalysis of the Bus-Motor-Failure Data. Technometrics 37, 436-445, 1995.
• Percontini, A. New Extended Lifetime Distributions, Ph. D. thesis in Computational mathematics, Federal University of Pernambuco, Brazil, 2014.
• Percontini, A., Cordeiro, G.M. and Bourguignon, M. The G-Negative Binomial Family: General Properties and Applications, Adv Appl Stat 35, 127-160, 2013.
• Percontini, A., Blas, B. and Cordeiro, G.M. The beta weibull poisson distribution, Chil J Stat 4 3-26, 2013.
• Pescim, R.R., Cordeiro, G.M., Dem´etrio, C.G.B. and Nadarajah, S. The new class of Kummer beta generalized distributions, SORT 36, 153-180, 2012.
• Ramos, M.W.A., Marinho, P.R.D., Cordeiro, G.M., Silva, R.V. and Hamedani, G. The kumaraswamy-G Poisson family of distributions, J Stat Theory Appl 14, 222-239, 2015.
• Silva, R.B., Bourguignon, M., Dias, C.R.B. and Cordeiro, G.M. The compound class of extended Weibull power series distributions, CSDA 58, 352-367, 2013.
• Silva, R.V., Gomes-Silva, F., Ramos, M.W.A., Cordeiro, G.M., Marinho, P.R.D. and Andrade, T.A.N. The Exponentiated Kumaraswamy-G Class: General Properties and Application, Rev Colomb Estad 2019, Forthcoming.
• Shakil, M., Kibria, B.M. and Singh, J.N. A new family of distributions based on the generalized Pearson differential equation with some applications, Aust J Stat 39, 259-258, 2010.
• Tahir, M.H. and Cordeiro, G.M. Compounding of distributions: a survey and new generalized classes, JSDA 3, 1-35, 2016.
• Tahir, M. H. and Nadarajah, S. Parameter induction in continuous univariate distributions: Well established G families, An Acad Bras Cienc 87, 539-568, 2015.
• Voda, V. G. A method constructing density functions: the case of a generalized Rayleigh variable, Appl Math 54, 417-431, 2009.
• Zografos, K. and Balakrishnan, N. On the families of beta-and generalized gamma-generated distribution and associated inference, Stat Met 6, 344-362, 2009.